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1.
张纯  仲政 《力学季刊》2006,27(4):668-674
利用混合微分求积法,对任意荷载作用下不同材料梯度分布的功能梯度材料平板柱形弯曲问题进行了分析。针对广义微分求积法求解集中荷载问题精度不高的缺点,本文利用小波微分求积法进行了改进。由于小波对突变信号具有良好的自适应描述能力,因此在平板宽度方向上,利用小波微分求积法可以有效地处理集中荷载;而在材料梯度变化的板厚方向上,则利用广义微分求积法计算量小且精度高的特点进行离散计算。计算表明,混合微分求积法不仅保留了广义微分求积法高效的特点,而且能有效地求解任意荷载作用的问题。通过算例,分析了在机械荷载作用下,材料不同梯度形式、平板上下表面材料性质差异对功能梯度平板结构响应的影响。  相似文献   

2.
基于小波微分求积法的薄板弯曲分析   总被引:2,自引:1,他引:1  
张纯  仲政 《计算力学学报》2008,25(6):863-867
利用小波微分求积法(WDQM)对任意荷载作用下的薄板弯曲问题进行了求解分析。数值算例表明,小波微分求积法与一般的DQ法相比具有很好的适用性,特别是薄板受集中荷载或不连续分布荷载作用时,由于小波基函数的紧支撑特性与其对突变信号良好的描述能力,WDQ法的精度明显优于一般的DQ法,具有良好的应用前景。  相似文献   

3.
为了评估人行荷载作用下梁式结构的振动舒适度,利用微分求积-积分求积,即DQ-IQ混合法求解移动荷载作用下梁的振动响应。人行荷载作用下梁式结构的振动控制方程是含Dirac函数的偏微分方程,首先利用IQ法离散与时间相关的Dirac函数,再利用DQ法把控制方程转化为二阶常系数微分方程,最后利用Newmark算法求解微分方程。以某钢结构连廊为例,利用DQ法计算结构自振频率并与解析解进行对比,结果验证了节点选取和边界条件施加的合理性,再利用DQ-IQ混合法和振型叠加法分别计算了不同行走步频下连廊的响应,计算结果表明,DQ-IQ混合法具有较高的可靠性和精确性。DQ-IQ混合法也可以推广到诸如车辆荷载作用下路面或桥梁的动力响应等其他移动荷载下结构的振动分析。  相似文献   

4.
为了评估人行荷载作用下梁式结构的振动舒适度,利用微分求积-积分求积,即DQ-IQ混合法求解移动荷载作用下梁的振动响应。人行荷载作用下梁式结构的振动控制方程是含Dirac函数的偏微分方程,首先利用IQ法离散与时间相关的Dirac函数,再利用DQ法把控制方程转化为二阶常系数微分方程,最后利用Newmark算法求解微分方程。以某钢结构连廊为例,利用DQ法计算结构自振频率并与解析解进行对比,结果验证了节点选取和边界条件施加的合理性,再利用DQ-IQ混合法和振型叠加法分别计算了不同行走步频下连廊的响应,计算结果表明,DQ-IQ混合法具有较高的可靠性和精确性。DQ-IQ混合法也可以推广到诸如车辆荷载作用下路面或桥梁的动力响应等其他移动荷载下结构的振动分析。  相似文献   

5.
丝束变角度复合材料具有变刚度的特点,因此其结构分析具有相当难度.本文采用状态空间法和微分求积法联合的半解析数值方法对丝束轴向变角度复合材料梁的弯曲问题进行研究.假设纤维方向角沿梁的轴向按照任意连续函数变化,选取位移和位移的一阶导数作为状态变量,建立了丝束轴向变角度复合材料梁弹性分析的状态空间方程,将状态变量对轴向坐标的导数采用微分求积法进行求解,进而可得问题的半解析数值解.通过与现有文献及ABAQUS计算结果的比较,验证了本文方法的正确性,并对微分求积法求解本问题的收敛性进行了分析.通过数值算例研究了纤维方向角沿梁轴向的变化对丝束轴向变角度复合材料梁的位移及应力分布的影响,研究结果可为该种结构的设计提供一定的参考.  相似文献   

6.
针对梁式结构受移动荷载作用的非平稳随机振动问题,提出了一种综合利用微分求积法和虚拟激励法DQ-PEM的新方法。梁式结构受移动荷载作用的振动控制方程为含Dirac函数的偏微分方程,利用微分求积(DQ)-积分求积法(IQ)法将其振动控制方程转化为不含Dirac函数的常微分方程。同时,将表示荷载位置变化的Dirac函数视为移动荷载的非平稳化函数,再结合虚拟激励法的思想,可得梁式结构在确定性荷载作用下的虚拟响应,进而得到其非平稳随机响应。通过工程算例验证了该方法的准确性与有效性,并进一步讨论了不同速度和不同边界条件下梁式结构受移动荷载作用的随机振动问题。  相似文献   

7.
基于应变梯度弹性理论,研究了静电激励MEMS微结构吸合电压的尺寸效应.利用最小势能原理分别推导出含尺寸效应的一维梁模型和二维板模型的高阶控制方程.采用广义微分求积法和拟弧长算法对控制方程进行了数值求解.结果表明,随着结构尺寸的降低,新模型所预测的归一化的吸合电压呈非线性增长,表现出尺寸效应(特别是当结构尺寸与内禀常数在...  相似文献   

8.
聂国隽  仲政 《力学季刊》2005,26(2):198-203
本文采用一种精确、简便的数值计算方法——微分求积单元法(DQEM)对变截面门式刚架结构进行了力学分析。首先建立了一般荷载作用下变截面构件的平衡微分方程,并采用微分求积法进行离散,进而得出了较为精确的分析变截面构件的单元力学模型。该模型的刚度方程不仅反映了单元的刚度性质,而且反映了单元的实际荷载作用,可较为精确地分析变截面门式刚架结构在分布载荷作用下的受力性能。通过与有限元法计算结果的比较,表明了微分求积单元法在变截面刚架的力学分析中的正确性和优越性。微分求积单元法可用于任意形状的刚架结构的静力分析。  相似文献   

9.
对于较厚的多层复合壳体,其振动位移沿厚度方向呈锯齿形变化且层间剪切和拉、压应力呈三维耦合状态,采用传统的等效单层理论分析已不能满足精度要求. 建立不受结构厚度、铺层材料性质和铺层方式限制的三维分析方法具有重要的研究价值. 本文以独立铺层为建模对象,结合广义谱方法与微分求积技术建立了一种适用一般边界条件和铺层方式的多层复合壳体三维分析新方法——谱--微分求积混合法. 该方法应用三维弹性理论对独立铺层进行精确建模,有效克服了二维简化理论对横向变形以及层间应力估计不确切的缺点;引入微分求积技术对铺层进行数值离散,将三维偏微分问题转化为二维偏微分问题,降低了求解维度和难度;应用广义谱方法近似地表述离散计算面上的场变量,将获取的二维偏微分方程转化为以场变量谱展开系数为未知量的线性代数方程组,避免了对超越方程的求解. 数值验证结果表明该方法收敛性好,计算精度高.   相似文献   

10.
采用广义微分求积法(GDQM)对钢筋混凝土(RC)梁进行了准静力分析,得到了其抗静载的强度特性.首先,基于虚功原理导出了考虑钢筋和混凝土材料的非线性的RC梁准静力分析控制微分方程,并根据广义微分求积法对其离散,从而得到有限自由度的非线性代数方程组,进而采用Newton-Raphson迭代求解格式,建立了荷载增量法数值分析模型.其次,通过本文GDQM与有限元法分析结果比较,表明了新建算法的正确性;与有限元法的收敛性对比表明本文算法较有限元法有优越性.  相似文献   

11.
The thermal vibration of functionally graded(FG) porous nanocomposite beams reinforced by graphene platelets(GPLs) is studied.The beams are exposed to the thermal gradient with a multilayer structure.The temperature varies linearly across the thickness direction.Three different types of dispersion patterns of GPLs as well as porosity distributions are presented.The material properties vary along the thickness direction.By using the mechanical parameters of closed-cell cellular solid,the variation of Poisson's ratio and the relation between the porosity coefficient and the mass density under the Gaussian random field(GRF) model are obtained.By using the Halpin-Tsai micromechanics model,the elastic modulus of the nanocomposite is achieved.The equations of motion based on the Timoshenko beam theory are obtained by using Hamilton's principle.These equations are discretized and solved by using the generalized differential quadrature method(GDQM) to obtain the fundamental frequencies.The effects of the weight fraction,the dispersion model,the geometry,and the size of GPLs,as well as the porosity distribution,the porosity coefficient,the boundary condition,the metal matrix,the slenderness ratio,and the thermal gradient are presented.  相似文献   

12.
This paper focuses on the buckling behaviors of a micro-scaled bi-directional functionally graded (FG) beam with a rectangular cross-section, which is now widely used in fabricating components of micro-nano-electro-mechanical systems (MEMS/NEMS) with a wide range of aspect ratios. Based on the modified couple stress theory and the principle of minimum potential energy, the governing equations and boundary conditions for a micro-structure-dependent beam theory are derived. The present beam theory incorporates different kinds of higher-order shear assumptions as well as the two familiar beam theories, namely, the Euler-Bernoulli and Timoshenko beam theories. A numerical solution procedure, based on a generalized differential quadrature method (GDQM), is used to calculate the results of the bi-directional FG beams. The effects of the two exponential FG indexes, the higher-order shear deformations, the length scale parameter, the geometric dimensions, and the different boundary conditions on the critical buckling loads are studied in detail, by assuming that Young’s modulus obeys an exponential distribution function in both length and thickness directions. To reach the desired critical buckling load, the appropriate exponential FG indexes and geometric shape of micro-beams can be designed according to the proposed theory.  相似文献   

13.
Due to the conflict between equilibrium and constitutive requirements,Eringen's strain-driven nonlocal integral model is not applicable to nanostructures of engineering interest. As an alternative, the stress-driven model has been recently developed. In this paper, for higher-order shear deformation beams, the ill-posed issue(i.e., excessive mandatory boundary conditions(BCs) cannot be met simultaneously)exists not only in strain-driven nonlocal models but also in stress-driven ones. The well-posedness of both the strain-and stress-driven two-phase nonlocal(TPN-Strain D and TPN-Stress D) models is pertinently evidenced by formulating the static bending of curved beams made of functionally graded(FG) materials. The two-phase nonlocal integral constitutive relation is equivalent to a differential law equipped with two restriction conditions. By using the generalized differential quadrature method(GDQM),the coupling governing equations are solved numerically. The results show that the two-phase models can predict consistent scale-effects under different supported and loading conditions.  相似文献   

14.
Abstract

This article contains the nonlocal elasticity theory to capture size effects in functionally graded (FG) nano-rod under magnetic field supported by a torsional foundation. Torque effect of an axial magnetic field on an FG nano-rod has been defined using Maxwell’s relation. The material properties were assumed to vary according to the power law in radial direction. The Navier equation and boundary conditions of the size-dependent FG nano-rod were derived by the Hamilton’s principle. These equations were solved by employing the generalized differential quadrature method (GDQM). Presented model has the ability to turn into the classical model if the material length scale parameter is taken to be zero. The effects of some parameters, such as inhomogeneity constant, magnetic field and small-scale parameter, were studied. As an important result of this study can be stated that an FG nano-rod model based on the nonlocal elasticity theory behaves softer and has smaller natural frequency.  相似文献   

15.
A nonlocal study of the vibration responses of functionally graded (FG) beams supported by a viscoelastic Winkler-Pasternak foundation is presented. The damping responses of both the Winkler and Pasternak layers of the foundation are considered in the formulation, which were not considered in most literature on this subject, and the bending deformation of the beams and the elastic and damping responses of the foundation as nonlocal by uniting the equivalently differential formulation of well-posed strain-driven (ε-D) and stress-driven (σ-D) two-phase local/nonlocal integral models with constitutive constraints are comprehensively considered, which can address both the stiffness softening and toughing effects due to scale reduction. The generalized differential quadrature method (GDQM) is used to solve the complex eigenvalue problem. After verifying the solution procedure, a series of benchmark results for the vibration frequency of different bounded FG beams supported by the foundation are obtained. Subsequently, the effects of the nonlocality of the foundation on the undamped/damping vibration frequency of the beams are examined.  相似文献   

16.
In this paper, the differential quadrature (DQ) method is presented for easy and effective analysis of isotropic functionally graded (FG) and functionally graded coated (FGC) thin plates with constant Poisson’s ratio and varying Young’s modulus in the thickness direction. The bending of FG and FGC plates under transverse loading has been studied using the polynomial differential quadrature (PDQ) and the harmonic differential quadrature (HDQ) methods. A three-dimensional elasticity solution for a moderately thick FG plate with exponential Young’s modulus is used as the benchmark. Two examples, including a thin FG rectangular plate and a thin FGC rectangular plate with sigmoidal Young’s modulus, are investigated. The numerical results of PDQ and HDQ methods reveal good agreement with other solutions. Also, it is shown that the formulations for thin FG plates and homogeneous plates are similar, except that the plane strain components of the middle surface in FG plates are not zero.  相似文献   

17.
Three-dimensional free vibration analysis of functionally graded piezoelectric (FGPM) annular plates resting on Pasternak foundations with different boundary conditions is presented. The material properties are assumed to have an exponent-law variation along the thickness. A semi-analytical approach which makes use of state-space method in thickness direction and one-dimensional differential quadrature method in radial direction is utilized to obtain the influences of the Winkler and shearing layer elastic coefficients of the foundations on the non-dimensional natural frequencies of functionally graded piezoelectric annular plates. The analytical solution in the thickness direction can be acquired using the state-space method and approximate solution in the radial direction can be obtained using the one-dimensional differential quadrature method. Numerical results are given to demonstrate the convergency and accuracy of the present method. The influences of the material property graded index, circumferential wave number and thickness of the annular plate on the dynamic behavior are also investigated. Since three-dimensional free vibration analysis of FGPM annular plates on elastic foundations has not been implemented before, the new results can be used as benchmark solutions for future researches.  相似文献   

18.
Abstract

In the present study, the high-order free vibration analysis of rotating fully-bonded and delaminated sandwich beams; with and without vertical contact; containing AL-foam flexible core and carbon nanotubes reinforced composite (CNTRC) face sheets subjected to thermal and moisture field are investigated by using generalized differential quadrature method (GDQM). The compressible core and face sheets of sandwich beam, respectively, are composed of Aluminum alloy foam with variable mechanical properties in the thickness direction and CNTRC with temperature dependent material properties. In this study, the high-order sandwich panel theory (HSAPT) for AL-foam flexible core and Euler-Bernoulli beam theory for CNTRC face sheets are considered. By employing Hamilton’s principle, the governing partial differential equations of motion and associated boundary and continuity conditions for various types of regions (fully-bonded, delaminated with contact, delaminated without contact) are derived and then discretized by using GDQM. The final formulations lead to 14 partial differential equations for the entire structure including five equations for fully-bonded two-headed parts of AL-foam cored sandwich beam (AL-FCSB) and four equations for delaminated middle part of AL-FCSB beam which are combined in axial and transverse deformations. A parametric study is performed to investigate the influence of some important parameters such as existence of delaminated region, type of delaminated region (with or without contact), longitudinal position of delaminated region, slenderness ratio, face sheet thickness ratio, CNT volume fraction, temperature rise, moisture concentration, rotating speed, and hub radius. The obtained results reveal that the 1st frequency of delaminated AL-FCSB beam, whether with or without vertical contact, is less remarkably than ones of fully-bonded AL-FCSB beam which its value for the case of delaminated ‘with contact’ is larger than that of ‘without contact’. Moreover, the 1st frequency variation of the delaminated AL-FCSB beam is symmetrical with regard to the longitudinal position of the debonded region such that the 1st natural frequency declines with moving the debonded region toward the center of the beam. The study of vibration behavior of rotating sandwich beams is very important in design of rotating structural systems, specially damaged ones, such as airplanes, helicopter rotor blades, and robot arms. One of the most important types of damage encountered in mentioned cases is the decomposition of two layers or delamination. Working these rotating structures in the media, are always along with variations of temperature and humidity and hence their mechanical properties may be changed due to the environment conditions.

Communicated by S. Velinsky  相似文献   

19.
The generalized differential quadrature method (GDQM) is employed to consider the free vibration and critical speed of moderately thick rotating laminated composite conical shells with different boundary conditions developed from the first-order shear deformation theory (FSDT). The equations of motion are obtained applying Hamilton’s concept, which contain the influence of the centrifugal force, the Coriolis acceleration, and the preliminary hoop stress. In addition, the axial load is applied to the conical shell as a ratio of the global critical buckling load. The governing partial differential equations are given in the expressions of five components of displacement related to the points lying on the reference surface of the shell. Afterward, the governing differential equations are converted into a group of algebraic equations by using the GDQM. The outcomes are achieved considering the effects of stacking sequences, thickness of the shell, rotating velocities, half-vertex cone angle, and boundary conditions. Furthermore, the outcomes indicate that the rate of the convergence of frequencies is swift, and the numerical technique is superior stable. Three comparisons between the selected outcomes and those of other research are accomplished, and excellent agreement is achieved.  相似文献   

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